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Simple Harmonic Motion
Spring
Equipment Needed for Spring Procedure
Clamp, Pendulum, Arbor Sci. P1-7139
Scale, Digital Sartorious BP-6100
Mass Hanger, 50g
Spring, Brass Harmonic Motion,
CENCO 160656
Mass Set, Gram Assorted
Stopwatch, Mychron #261
Meter Stick
Introduction
Any motion that repeats itself in equal intervals of time is called periodic motion.
A special form of periodic motion is called Simple Harmonic Motion (SHM). Simple
Harmonic Motion is defined as cyclical or oscillatory motion in which the resultant force
on the oscillating body at any instant is directly proportional to its displacement from the
"rest position" and opposite in direction to its motion. Mathematically this can be
written as:
F  kx
Equation 1
where
F is the resultant force on the oscillating body,
x is the displacement from equilibrium, and
k is a constant called the “spring constant
This force is a "restoring force" because it tends to restore the oscillating body back to its
original position.
Examples of simple harmonic motion include oscillations of a mass on a spring.
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The period of oscillation depends on the parameters of the system. For a mass on a
spring, this is given by:
T  2
m
k
Equation 2
where
m is the suspended mass and
k is the spring constant.
Procedure
1. Determine the spring constant, k.
Suspend different known weights from the spring and measure the elongation of the
spring. Plot the force as a function of the stretch in the spring. The slope will be the
spring constant, k.
Data Step 1
Mass
(kg)
0.05kg
X
(m)
Force
(N)
0.07kg
0.09kg
0.11kg
0.13kg
N/m
2. Start the spring oscillating, timing 20 oscillations with a stopwatch. Repeat by adding
20-gram weights to the hanger. Calculate the period and the period squared for each
mass and record in the table. Plot T2 vs. mass (mass is the hanging mass) and find the
slope of the line.
From Equation 2
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Data Step 2
T for 10
oscillations
(s)
Period T
(s)
Hanging
mass
T2
(s2)
0.05 kg
0.07 kg
0.09 kg
0.11 kg
0.13 kg
Spring Constant, k, from slope
Error
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